When
Where
Speaker: Yulia Peet, Arizona State University
Title: Partial Integral Equations for Analysis, Control and Simulation of PDEs
Abstract: This talk discusses a new representation of Partial Differential Equations (PDEs) in a form of Partial Integral Equations (PIEs). PIE form allows us to remove boundary constraints from the solution domain and instead embed them into the construction of Partial Integral Operators that govern the PIE dynamics, all through an analytical transformation. The significance of this transformation is that many theoretical and numerical problems involved with the imposition of boundary and interface conditions during the solution of PDE systems can now be avoided. The framework is very general and is applicable to a large class of linear (and potentially nonlinear) PDEs with versatile boundary conditions; moreover, the transformation formulas are generalizable and are automated in a recently developed software PIETOOLs that can transform a user-defined PDE (or their system) to a PIE in a matter of seconds. The talk discusses linear 1D and 2D PDEs and presents efficient high-order numerical techniques based on Chebyshev methods that we developed for their solution as PIEs. We highlight the usability of PIE approach for stability analysis and control of PDE systems, including fluid flow problems.